What are the limitations of the first law of thermodynamics?

The amount of work,which can be obtained by supplying $200 \, cal$ of heat,is

An engineer claims to have made an engine delivering $10 \ kW$ of power with a fuel consumption of $1 \ g/s$. The calorific value of the fuel is $2 \ kcal/g$. Is the claim of the engineer valid?

The figure shows a cylindrical adiabatic container of total volume $2V_0$ divided into two equal parts by a conducting piston (which is free to move). Each part contains an identical gas at pressure $P_0$. Initially,the temperature of the left and right parts is $4T_0$ and $T_0$ respectively. An external force is applied on the piston to keep it at rest. Find the value of the external force required when thermal equilibrium is reached. ($A =$ Area of the piston)

For an ideal gas with initial pressure and volume $p_{i}$ and $V_{i}$ respectively, a reversible isothermal expansion occurs until its volume becomes $V_{0}$. Then, it is compressed to its original volume $V_{i}$ by a reversible adiabatic process. If the final pressure is $p_{f}$, then which of the following statement(s) is/are true?

Two cylinders of equal size are filled with an equal amount of ideal diatomic gas at room temperature. Both cylinders are fitted with pistons. In cylinder $A$,the piston is free to move (isobaric process),while in cylinder $B$,the piston is fixed (isochoric process). When the same amount of heat is supplied to both cylinders,the temperature of the gas in cylinder $A$ rises by $30\, K$. What will be the rise in temperature of the gas in cylinder $B$ (in $;K$)?